Question

сократите дробь
1)2m^2-72n^2(4m+24n)^2
2)a^2-8ab-a-2b+2
3)a^3+2a^2b+ab^2a^3-ab^2

Answer 1

$1)frac{2m^2-72n^2}{(4m+24n)^2} = frac{2(m^2-36n^2)}{(4(m+6n))^2}=frac{2(m-6n)(m+6n)}{16(m+6n)^2}=frac{(m-6n)}{8(m+6n)}$

$2) frac{a^3-8}{ab-a-2b+2}=frac{a^3-8}{a(b-1)-2(b-1)}=frac{(a-2)(a^{2} +2a+4)}{(a-2)(b-1)}=frac{(a^2+2a+4)}{(b-1)}$

$3) frac{a^3+2a^2b+ab^2}{a^3-ab^2} =frac{a(a^2+2ab+b^2)}{a(a^{2} -b^2)}= frac{(a+b)^{2}}{(a -b)(a+b)}= frac{a+b}{a-b}$